Typical jet systems


F-curve, i-curve, and A-curve for a typicai system  [c.689]

Figure 8-14. E-curve, F-curve, and A-curve for a typicai system with dead space. Figure 8-14. E-curve, F-curve, and A-curve for a typicai system with dead space.
Figure 8-15. E-curve and F-curve for a typicai system with channeiing. Figure 8-15. E-curve and F-curve for a typicai system with channeiing.
The preceding material of this section has focused on the most important phenomenological equation that thermodynamics gives us for multicomponent systems—the Gibbs equation. Many other, formal thermodynamic relationships have been developed, of course. Many of these are summarized in Ref. 107. The topic is treated further in Section XVII-13, but is worthwhile to give here a few additional relationships especially applicable to solutions.  [c.76]

The topic of spreading rates is of importance in the technology of the use of mono-layers for evaporation control (see Section IV-6) it is also important, in the opposite sense, in the lubrication of fine bearings, as in watches, where it is necessary that the small drop of oil remain in place and not be dissipated by spreading. Zisman and coworkers have found that spreading rates can be enhanced or reduced by the presence of small amounts of impurities in particular, strongly adsorbed surfactants can form a film over which the oil will not spread [48].  [c.111]

Microemulsions are treated in a separate section in this chapter. Unlike macro- or ordinary emulsions, microemulsions are generally thermodynamically stable. They constitute a distinctive type of phase, of structure unlike ordinary homogeneous bulk phases, and their study has been a source of fascination. Finally, aerosols are discussed briefly in this chapter, although the topic has major differences from those of emulsions and foams.  [c.500]

To proceed with the topic of this section. Refs. 250 and 251 provide oversights of the application of contemporary surface science and bonding theory to catalytic situations. The development of bimetallic catalysts is discussed in Ref. 252. Finally, Weisz [253] discusses windows on reality the acceptable range of rates for a given type of catalyzed reaction is relatively narrow. The reaction becomes impractical if it is too slow, and if it is too fast, mass and heat transport problems become limiting.  [c.729]

A topic of current interest is that of methane activation to give ethane or selected oxidation products such as methanol or formaldehyde. Oxide catalysts are used, and there may be mechanistic connections with the Fischer-Tropsch system (see Ref. 285).  [c.732]

For very fast reactions, as they are accessible to investigation by pico- and femtosecond laser spectroscopy, the separation of time scales into slow motion along the reaction path and fast relaxation of other degrees of freedom in most cases is no longer possible and it is necessary to consider dynamical models, which are not the topic of this section. But often the temperature, solvent or pressure dependence of reaction rate  [c.851]

The scope of this section restricts the discussion. One omitted topic is the collision and interaction of molecules with surfaces (see [20, 21] and section A3.9). This topic coimects quantum molecular dynamics in gas and condensed phases. Depending on the time scales of the interaction of a molecule witli a surface, the  [c.2291]

Both the electronic and the geometry optimization problem, particularly the latter, may have more than one solution. For small, rigid molecules, tire approximate molecular geometry is chemically obvious, and the presence of multiple minima is not a serious concern. For large, flexible molecules, however, finding the absolute minimum, or a complete set of low-lying equilibrium structures, is only a partially solved problem. This topic will be discussed in the last section of this chapter. The rest of the article deals with local optimization, i.e., finding a minimum from a reasonably close starting point. We will also discuss the detennination of other stationary points—most importantly saddle points-constrained optimization, and reaction paths. Several reviews have been published on geometry optimization [1, 2]. The optimization of SCF-type wavefiinctions is often highly nonlinear, particularly for the multiconfigurational case, and this has received most attention [3, 4].  [c.2332]

It is of course futile to attempt to cover all of biophysical chemistry within one short chapter. The emphasis will be on necessary concepts, especially where these diverge from the mainstream of physical chemistry inevitably there will be gaps. Material which is well known and readily found in standard texts (e.g. [11]), or in other chapters of this encyclopaedia, will be dealt with cursorily, if at all, but new material, and topics less well known than they should be, are accorded a more detailed treatment. Given the central role of macromolecular interactions in biological systems, they are covered extensively (section C2.14.6 and section C2.14.7 and part of section C2.14.3), except for protein folding (section C2.14.2) since it is also the topic of chapter 2.5. Biological membranes and associated topics such as the conduction of the nervous impulse [14,15] will not be discussed. Another omission is the interaction of light with biological molecules, because it does not seem that in essence they diverge significantly from photochemical processes in general, without excluding the possibility that photons may be involved in intercellular signalling. For the same reason, intra- and intennolecular electron transfer phenomena have also been omitted.  [c.2817]

Almost all aspects of the field of chemistry involve tire flow of energy eitlier witliin or between molecules. Indeed, tire occurrence of a chemical reaction between two species implies tire availability of some minimum amount of energy in tire reacting system. The study of energy transfer processes is tluis a topic of fundamental importance in chemistry. Energy transfer in gases is of particular interest partly because very sophisticated methods have been developed to study such events and partly because gas phase processes lend tliemselves to very complete and detailed tlieoretical analysis.  [c.2996]

Interestingly, the need for a multiple electronic set, which we connect with the reciprocal relations, was also a keynote of a recent review ([46] and previous publications cited there and in [47]). Though the considerations relevant to this effect are not linked to the complex nature of the states (but rather to the stability of the adiabatic states in the real domain), we have included in Section HI a mention of, and some elaboration on, this topic.  [c.97]

At this point, it is instructive to discuss the distinction between molecules, anchors, and quantum mechanical wave functions that represent them. The topic is best introduced by using an example. Consider the H4 system [34].  [c.333]

Although this reaction appears to involve only two electrons, it was shown by Mulder [57] that in fact two jc and two ct elections are required to account for this system. The three possible spin pairings become clear when it is realized that a pair of carbene radicals are formally involved. Figure 14. In practice, the conical intersection defined by the loop in Figme 14 is high-lying, so that often other conical intersections are more important in ethylene photochemistry. Flydrogen-atom shift products are observed [58]. This topic is further detailed in Section VI.  [c.350]

It has been observed by [27, 24] that the equations of motion of a free rigid body are subject to reduction. (For a detailed discussion of this interesting topic, see [23].) This leads to an unconstrained Lie-Poisson system which is directly solvable by splitting, i.e. the Euler equations in the angular momenta  [c.356]

Representation of such a system by a connection tabic having bonds between the iron atom and the five carbon atoms of either one of the two cyclopentadienyl rings is totally inadequate. A few other examples of structures that can no longer be adequately described by a standard connection table are given in the Section 2.G.2.  [c.64]

A wider variety of reaction types involving reactions at bonds to oxygen atom bearing functional groups was investigated by the same kind of methodology [30]. Reaction classification is an essential step in knowledge extraction from reaction databases. This topic is discussed in Section 10.3.1 of this book.  [c.196]

A central - and primary - task in deriving knowledge from information on reaction instances contained in databases is the grouping of such instances into reaction types. The topic of reaction classification has already been treated in Section 3.5, and readers are encouraged to consult this section again. Particularly, the data-driven approaches to reaction classification aim at directly using the information contained in reaction databases for generalizations to allow predictions on the course of chemical reactions by analogy.  [c.544]

During the work described in this thesis, we were confronted with two topics that warrant general comments. The first involves the interaction between Lewis acids and Lewis bases in aqueous solution. Although enthusiasm for use of water as a medium for Lewis-acid catalysed reactions is rising rapidly, it is appropriate to address some of the problems that are too often overlooked, but are likely to be encountered using this very special solvent. Section 6.3 elaborates on these problems The second topic concerns hydrophobic effects. When working with relatively apolar compounds in water, as we did in this study, hydrophobic effects are ubiquitous. A deeper understanding of these effects would be of great help in recognising and employing them in organic chemistry. Fortunately, after decades of extensive discussions, it seems as if a consistent molecular picture is now emerging, which will be outlined in Section 6.4.  [c.161]

The protons in 1 chloro 1 cyanoethene are diastereo topic (Section 13 6) They are nonequivalent and have dif ferent chemical shifts Re member splitting can only occur between protons that have different chemical shifts  [c.542]

The protons in 1-chloro-1-cyanoethene are diastereo-topic (Section 13.6). They are nonequivalent and have different chemical shifts. Remember, splitting can only occur between protons that have different chemical shifts.  [c.542]

Wetting behavior on rough surfaces is an important topic for many practical applications. Analytical models provide an equilibrium interface shape as a function of the film thickness and interaction potential [20]. Harden and Andleman have investigated thermal fluctuations on the surface of films on rough solids and found, as one might expect, that for thick films the surface fluctuations were dominated by capillary waves (see Section IV-3C) while thin films had surface waves correlated with the solid surface roughness [21]. Experimental measurements of the thickness by x-ray reflectivity [18] are in general agreement with models. Fermigier and co-workers have studied wetting on heterogeneous surfaces in a nairow Hele-Shaw cell having defects made by ink droplets [21a]. Air bubbles remained trapped on the defect as a result of contact line pinning (see Section X-5A).  [c.467]

As usual, there are complications in the details. The inverse 6th power term in Eq. XVII-88 for the dispersion attraction is not accurate at small distances since higher-order terms become significant (note Eq. VI-19). The corrugation of the surface, either topological or energetic, makes the interpretation of scattering experiments complicated. In the case of polyatomic adsorbates, U(z) also depends on the molecular orientation and in calculating the coefficient for the dispersion term, bond as well as atomic polarizabilities must be known. The case of molecular solids as adsorbents is interesting. Here, there are no broken bonds at the surface, nor ions. The results for N2 adsorbed on NH3, CO2, CH3OH and I2 did not agree with dispersion theory [105,106]. There are surface bond dipoles, however, and perhaps dipole-induced dipole interactions were important. Finally, physisorption on metals has been a difficult subject to treat. While experimental potentials have been obtained, the theory is made complicated by the matter of image forces, and the approach is now rather quantum-mechanical, such as using density functional theory (see Section XVIII-6A). References 8, 104, and 107 discuss the topic.  [c.638]

The plan of this chapter is as follows. We discuss chemisorption as a distinct topic, first from the molecular and then from the phenomenological points of view. Heterogeneous catalysis is then taken up, but now first from the phenomenological (and technologically important) viewpoint and then in terms of current knowledge about surface structures at the molecular level. Section XVIII-9F takes note of the current interest in photodriven surface processes.  [c.686]

When a system is not in equilibrium, the mathematical description of fluctuations about some time-dependent ensemble average can become much more complicated than in the equilibrium case. However, starting with the pioneering work of Einstein on Brownian motion in 1905, considerable progress has been made in understanding time-dependent fluctuation phenomena in fluids. Modem treatments of this topic may be found in the texts by Keizer [21] and by van Kampen [22]. Nevertheless, the non-equilibrium theory is not yet at the same level of rigour or development as the equilibrium theory. Here we will discuss the theory of Brownian motion since it illustrates a number of important issues that appear in more general theories.  [c.687]

The interaction of light with both clean surfaces and those having adsorbed species has been a popular research topic over the past 10 years [94]- Our understanding of processes such as photodesorption, photodissociation and photoreaction is still at a very early stage and modelling has been largely perfonned on a system-by-system basis rather than any general theories being applicable. One of the most important aspects of perfomiing photochemical reactions on surfaces, which has been well documented by Polanyi and coworkers is that it is possible to align species before triggering reactions that caimot be done in the gas phase. This is frequently referred to as surface aligned photochemistry [95]. One of the key issues when light, such as that from a picosecond laser, impinges a surface covered with an adsorbate is where the actual absorption takes place. Broadly speaking there are two possible choices either in the adsorbate molecule or the surface itself Unfortunately, although it may seem that um-avelling microscopic reaction mechanisms might be quite distinct depending on what was absorbing, this is not the case and considerable effort has been spent on deciding what the dynamical consequences are for absorption into either localized or extended electronic states [96].  [c.915]

A completely difierent approach to scattering involves writing down an expression that can be used to obtain S directly from the wavefunction, and which is stationary with respect to small errors in die waveftmction. In this case one can obtain the scattering matrix element by variational theory. A recent review of this topic has been given by Miller [32]. There are many different expressions that give S as a ftmctional of the wavefunction and, therefore, there are many different variational theories. This section describes the Kohn variational theory, which has proven particularly useftil in many applications in chemical reaction dynamics. To keep the derivation as simple as possible, we restrict our consideration to potentials of die type plotted in figure A3.11.1(c) where the waveftmcfton vanishes in the limit of v -oo, and where the Smatrix is a scalar property so we can drop the matrix notation.  [c.968]

As noted above, the coordinate system is now recognized as being of fimdamental importance for efficient geometry optimization indeed, most of the major advances in this area in the last ten years or so have been due to a better choice of coordinates. This topic is seldom discussed in the mathematical literature, as it is in general not possible to choose simple and efficient new coordinates for an abstract optimization problem. A nonlmear molecule with N atoms and no  [c.2341]

In what is called BO MD, the nuclear wavepacket is simulated by a swarm of trajectories. We emphasize here that this does not necessarily mean that the nuclei are being treated classically. The difference is in the chosen initial conditions. A fully classical treatment takes the initial positions and momenta from a classical ensemble. The use of quantum mechanical distributions instead leads to a seraiclassical simulation. The important topic of choosing initial conditions is the subject of Section II.C.  [c.258]

The important enquiry into long time scales has also been a subject of interest over many years, but the progress has been slow. Computer capabilities have increased so rapidly that it has often been worthwhile to wait a few years to obtain the required increase in speed with standard methods rather than invent marginal improvements by faster algorithms or by using reduced systems. Many attempts to replace the time-consuming solvent molecules by potentials of mean force (see for example [32]) or to construct an appropriate outer boundary without severe boundary effects [43, 34] have been made, but none of these are fully satisfactory. Really slow events cannot be modeled by such simplifications a drastic reduction in the number of degrees of freedom is needed. When events are slow because an identifiable barrier must be crossed, good results can be obtained by calculating the free energy at the barrier in one or a few degrees of freedom. However, when events are slow because a very large multidimensional configurational space must be explored (as in protein folding or macromolecular aggregation), the appropriate methods are still lacking. We shall return to this important topic in Section 3.3.  [c.5]

The preceding section gave a briefintroduction to the handling of the stereochemistry of molecules by permutation group descriptors. Here we discuss this topic in more detail. The treatment is largely based on ideas introduced in Ref. [100],  [c.85]

The preceding chapters of this book deal with methods for representing chemical structures and reactions. As there is a huge and continuously increasing amount of data associated with chemical compoxmds, it is impossible to handle moxmtains of data by conventional techniques. The multi-feceted information on compounds, such as literature, physicochemical properties, spectra, etc., and on reactions can be handled in a comprehensive manner only by electronic methods. Such a system for storing and retrieving these data is generally called an information system (Figure 5-1), and comprises application programs (e.g., search engines) and a data stock or database, which can also be part of a database system. In chemistry the term database is often used for an entire information system, a database system, or a data-file itself. In this chapter, database is employed as a synonym for the entire information system. As models, languages, and management systems of databases fill volumes of books, this chapter can only give a flavor of this topic. For further literature, see Refs. [1-3].  [c.227]

A hierarchical system is the simplest type ofdatabase system. In this form, the var-iou.s data typc.s also called entities (sec figure 5-,3) arc as.signcd. systematically to various levels (Figure 5-5). The hierarchical system is represented as an upside-down tree with one root segment and ordered nodes. Each parent object can have one or more children (objects) but each child has only one parent. If an object should have more than one parent, this entity has to be placed a second time at another place in the database system.  [c.232]

Niek Buurma and Theo Rispens are most gratefully acknowledged for the inspiring discussions on hydrophobic effects. These discussions have contributed significantly to a better understanding of this topic and form the basis of what is described in Section 1.3.  [c.32]

The aliphatic -amino acids induce a reduction of the equilibrium constant for binding of the dienophile to the copper ion by roughly 50 %, as anticipated on the basis of statistics. However, when L-phenylalanine is used as ligand, this reduction is significantly less pronounced. For L-tyrosine, L-tryptophan and derivatives thereof, the equilibrium constant is even larger than that of the copper aquo ion. Compared to the most bulky of the aliphatic -amino acids, L-leucine ( G oornpi = -15.5 kJ/mole), L-abrine ( G (iompi= -21.1 kJ/mole) enhances the affinity of the catalyst for the dienophile by 5.6 kJ/mol. This enhancement cannot be attributed to a steric effect, since an increase of steric bulk (going from L-glycine, to L-valine, to L-leucine) leads to a modest reduction of IQ. Most likely, a specific interaction between the aromatic system of the -amino acid ligand and that of the coordinated dienophile (arene-arene interaction ) is responsible for the enhanced stability of the ternary complex (see Scheme 3.9). This type of ligand - ligand interaction is well documented. The most relevant literature on this topic is summarised in Section 3.2.3.  [c.87]

One measure of the strength of a bond is its bond dissoa ation energy This topic will be introduced in Section 4 16 and applied to ethylene in Section 5 2  [c.91]


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Rules of thumb for chemical engineers  -> Typical jet systems